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Question About Direct Sums and Dimension

score 33 · Answer 1 · 2026-04-16 07:50:41

33

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Question About Direct Sums and Dimension

Published on 16 Apr 2026 - 7:50

score 990 · Answer 2 · 2026-05-10 21:09:25

990

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Associativity of direct sums

Published on 10 May 2026 - 21:09

score 199 · Answer 3 · 2026-04-14 17:40:11

Let $R$ be a ring, $M$ an $R$-module, and $A, B ≤ M$ two submodules of $M$ such that $M = A ⊕ B$. Prove that $M/A \cong B$.

score 319 · Answer 4 · 2026-04-13 01:04:34

319

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Direct Sum and Diagonalization with a Linear Map

Published on 13 Apr 2026 - 1:04

score 64 · Answer 5 · 2026-04-17 10:54:58

64

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If $S_1,S_2,S_3$ have direct sum, then, $S_1 = (S_1+S_2) \cap (S_1+S_3)$?

Published on 17 Apr 2026 - 10:54

score 993 · Answer 6 · 2026-04-13 05:27:51

993

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Let $T: V \to V$ be a linear map such that $T^2-3T+2I=0$.

Published on 13 Apr 2026 - 5:27

score 79 · Answer 7 · 2026-04-17 01:05:22

79

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A different definition of coproduct in a category

Published on 17 Apr 2026 - 1:05

score 46 · Answer 8 · 2026-04-12 04:59:54

46

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Clarifying $\oplus$ notation for modules and vector spaces?

Published on 12 Apr 2026 - 4:59

score 361 · Answer 9 · 2026-04-11 20:12:15

361

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Direct sum of Banach Spaces

Published on 11 Apr 2026 - 20:12

score 72 · Answer 10 · 2026-04-16 10:42:21

72

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If $M$ has a largest proper submodule, then $ M$ is directly indecomposable

Published on 16 Apr 2026 - 10:42

score 815 · Answer 11 · 2026-04-12 14:06:45

815

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Does a direct subtraction of vector subspaces make sense?

Published on 12 Apr 2026 - 14:06

score 85 · Answer 12 · 2026-04-17 10:06:01

$M_1$, $M_2$ are submodules of a module $M$, then $M = M_1 + M_2$ and $M_1 \cap M_2 = 0$ implies M is isomorphic to $M_1 \oplus M_2$?

score 128 · Answer 13 · 2026-04-30 11:16:59

128

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Finite Length Modules

Published on 30 Apr 2026 - 11:16

score 56 · Answer 14 · 2026-04-15 19:37:21

56

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How to show that if $X=M \oplus N$ is a Banach space then $\exists c > 0$ $\forall m\in M \, \forall n\in N: ||m||+||n|| \leq c ||m+n||$?

Published on 15 Apr 2026 - 19:37

score 365 · Answer 15 · 2026-04-16 13:59:45

365

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If $AB=0$ for two commuting linear operators and their kernels intersect trivially, do they span the whole vector space?

Published on 16 Apr 2026 - 13:59

List Question

Question About Direct Sums and Dimension

Associativity of direct sums

Let $R$ be a ring, $M$ an $R$-module, and $A, B ≤ M$ two submodules of $M$ such that $M = A ⊕ B$. Prove that $M/A \cong B$.

Direct Sum and Diagonalization with a Linear Map

If $S_1,S_2,S_3$ have direct sum, then, $S_1 = (S_1+S_2) \cap (S_1+S_3)$?

Let $T: V \to V$ be a linear map such that $T^2-3T+2I=0$.

A different definition of coproduct in a category

Clarifying $\oplus$ notation for modules and vector spaces?

Direct sum of Banach Spaces

If $M$ has a largest proper submodule, then $ M$ is directly indecomposable

Does a direct subtraction of vector subspaces make sense?

$M_1$, $M_2$ are submodules of a module $M$, then $M = M_1 + M_2$ and $M_1 \cap M_2 = 0$ implies M is isomorphic to $M_1 \oplus M_2$?

Finite Length Modules

How to show that if $X=M \oplus N$ is a Banach space then $\exists c > 0$ $\forall m\in M \, \forall n\in N: ||m||+||n|| \leq c ||m+n||$?

If $AB=0$ for two commuting linear operators and their kernels intersect trivially, do they span the whole vector space?

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